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The kinetics of dynamic recrystallization of a low carbon vanadium-nitride microalloyed steel
Materials Science & Engineering A 604 (2014) 117–121
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
The kinetics of dynamic recrystallization of a low carbon vanadium-nitride microalloyed steel Baochun Zhao a,n, Tan Zhao a, Guiyan Li a, Qiang Lu b a b
Technology Center of Angang Steel Company Ltd., Anshan, Liaoning 114001, China Angang Steel Company Ltd., Bayuquan Subsidiary Company, Yingkou, Liaoning 115007, China
art ic l e i nf o
a b s t r a c t
Article history: Received 9 January 2014 Received in revised form 2 March 2014 Accepted 5 March 2014 Available online 12 March 2014
Single-pass compression tests were performed on a Gleeble-3800 thermo-mechanical simulator to study the dynamic recrystallization behavior of a low carbon vanadium-nitride microalloyed steel at the temperature in the range from 900 1C to 1050 1C and strain rate in the range from 0.1 s 1 to 10 s 1. Based on the flow curves from the tests, the effects of temperature and strain rate on the dynamic recrystallization behavior were analyzed. With the assistance of the process parameters, constitutive equations were used to obtain the activation energy and hot working equation. The strain hardening rate versus stress curves were used to determine the critical stress (strain) or the peak stress (strain). The dependence of the characteristic values on Zener–Hollomon was found. The dynamic recrystallization kinetics model of the tested steel was constructed and the validity was confirmed based on the experimental results. & 2014 Elsevier B.V. All rights reserved.
Keywords: Low carbon vanadium-nitride microalloyed steel Dynamic recrystallization Flow stress Mathematical model
1. Introduction Material microstructure evolution and flow behavior are complex during hot forming processes, which have a close relation to the shape of flow curves. Dynamic recovery (DRV), dynamic recrystallization (DRX) and static recrystallization (SRX) processes can be identified from the flow curves. Therefore, flow curves are often used to study the flow behavior of materials, which is also an efficient approach to study DRX behavior. Since DRX process contributes to grain refinement and lower stress, which play an important role in the formability, microstructure and mechanical properties of materials [1], it is of great practical importance to study the DRX that occurs during hot forming processes. At present, there are a considerable amount of researches on the DRX behavior of vanadium microalloyed steels or vanadium and titanium microalloyed steels [2,3]. In general, the steels with higher vanadium and lower nitrogen addition were tested. However, there are few researches on the steel with lower vanadium and higher nitrogen addition. Furthermore, it has been reported that nitrogen is a cost effective microalloyed element in vanadium microalloyed steel and it plays an important role in the effect of vanadium on the microstructure or properties of steels [4,5].
n Corresponding author at: Technology Center of Angang Steel Company Ltd., Anshan, Liaoning 114001, China. Tel.: þ86 41 2672 4152. E-mail address: [email protected] (B. Zhao).
http://dx.doi.org/10.1016/j.msea.2014.03.019 0921-5093/& 2014 Elsevier B.V. All rights reserved.
In the present work, single-pass compression tests were performed on a Gleeble-3800 thermo-mechanical simulator to study the DRX behavior of a low carbon vanadium-nitride microalloyed steel. Based on the flow curves, the effects of temperature and strain rate on the DRX behavior of the tested steel were analyzed. The DRX kinetics equations of the tested steel were established by the regression method. At last, the predicted results and experimental ones were compared.
2. Material and experiments In this work, the low carbon vanadium microalloyed steel with chemical composition of C 0.19, Mn 1.5, Si 0.37, V 0.06, Ti 0.019, S 0.0095, P 0.0087, N 0.0160 and balance iron (wt%) was used. The tested steel was from the continuous casting slab as received. The specimens with height of 12 mm and diameter of 8 mm were prepared. In order to reduce the occurrence of inhomogeneous compression, special anvils were employed. Both ends of the specimen were covered with tantalum foils to prevent adhesion between specimen and anvils. The specimens were austenitized at 1150 1C for 5 min and cooled with the rate of 5 1C/s to deformation temperature and held there for 1 min before compression. Single-pass compression tests were carried out at the temperature in the range from 900 to 1050 1C with an interval of 50 1C and strain rates of 0.1, 1, 3 and 10 s 1.
118
B. Zhao et al. / Materials Science & Engineering A 604 (2014) 117–121
3. Results and discussion 3.1. Flow curves analysis
mathematically smooth and there are some irregularities and fluctuations, which can make it impossible for the following differentiations. To eliminate the irregularities and fluctuations in the experimental curves, the flow curves were fitted by the ninth-order polynomial and good fitting curves were obtained. The resultant strain hardening rate θ versus stress curves are shown in Fig. 2. The inflection points and the zero points in the curves are marked out. Therefore, the critical stress sc (strain εc) or the peak stress sp (strain εp) can be obtained. Fig. 3 presents the relationship between sc (εc) and sp (εp). A linear relationship is recognizable and R is the linear correlation coefficient. By linear regression, the following formulas can be obtained:
Fig. 1 presents the flow curves under different deformation conditions. At the early stage of deformation, the stress increases proportionally to the strain, which leads to the increase in dislocation density and distortion in the steel. The strain hardening process is identified. At the second stage, the strain hardening effect can be reduced due to dislocation slipping, rearranging or eliminating. And the strain hardening rate keeps falling with the increase in strain. When the strain hardening rate is equal to zero, the stress reaches the peak. In Fig. 1, the flow curves exhibit typical peaks at the lower strain rate of 0.1 s 1. At the same strain rate and strain, the stress or the peak stress increases with the decrease in temperature. Since dislocation movement is restrained at lower temperature, it contributes to a higher strain hardening rate and results in a higher stress. At higher strain rate, strain hardening and dynamic recovery play the main role and no typical peak is recognizable. In Fig. 1b, it can be seen that the flow curve corresponding to strain hardening and dynamic recovery process is typical at a strain rate higher than 3 s 1.
In Sellars' research [9], the ratio of critical strain to peak strain generally falls in the range of 0.6–0.85. However, lower values for some microalloyed steel have been reported and they are in the range of 0.4–0.55 [10,11]. Since 0.4804 falls in the range, it is reasonable. Compared with the previous work on vanadium microalloyed steel [12], the value is higher, which maybe related to the higher nitrogen addition.
3.2. Determination of critical conditions
3.3. Activation energy and hot working equation
Poliak and Jonas [6,7] have proposed the critical condition kinetics based on the thermal irreversible principles and the critical conditions for the initiation of DRX can be determined by analyzing the relation between strain hardening rate and flow stress. It is a easier approach and widely used [7,8]. At the beginning of deformation, the softening induced by DRV is fast and strain hardening rate decreases with the increase of stress, which corresponds to the beginning of the sub-grain formation. At the second stage of deformation, the increase rate of softening rate decreases during the sub-grain forming process. When the stress reaches a critical value, the increase rate of softening rate suddenly increases due to onset of DRX, which leads to an inflection in the plot of strain hardening rate versus stress. The stress at the inflection point is identified as the critical stress. When a balance between strain hardening and softening reaches, the strain hardening rate would reduce to zero and the corresponding stress is identified as the peak stress. The flow curves under different deformation conditions were processed and analyzed by this method to determine the critical conditions of the tested steel. The experimental curves are not
The flow stress of material is related to process parameters and chemical compositions during hot working processes. With
sc ¼ 0:90285sp
ð1Þ
εc ¼ 0:48046εp
ð2Þ
Strain hardening rate θ
0.1s-1
σc
σp
Fig. 2. Strain hardening curves of the tested steel at different temperatures.
Fig. 1. Flow curves obtained for different deformation conditions.
B. Zhao et al. / Materials Science & Engineering A 604 (2014) 117–121
119
220 0.20
200
0.18
180
σc=0.90285σp
εc=0.48046εp
0.16
εc
σc
160 140
0.14
120
R=0.99253
0.12
100
0.10
80 80
100
120
140
160
σp
180
200
220
240
0.15
0.20
0.25
0.30
εp
0.35
0.40
.
3
3
2
2
1
1
ln (ε/s-1)
ln (ε/s-1)
Fig. 3. Relations between critical stress and peak stress (a); critical strain and peak strain (b).
0
.
-1 -2
0 -1 -2
-3 4.4
4.6
4.8
5.0
5.2
5.4
5.6
-3
80
100
120
140
ln(σp/Mpa)
160
180
200
220
240
260
σp/Mpa
Fig. 4. Relations between ln ε_ and ln sp (a); ln ε_ and sp (b).
chemical compositions unchanged, the dependence of temperature, strain rate and stress can be expressed as [13] Q ð3Þ A½ sinhðαsp Þn ¼ ε_ exp RT To obtain parameter α, the following formulas are also used: Q 0 A0 snp ¼ ε_ exp RT A″ expðβsp Þ ¼ ε_ exp
Q RT
ð4Þ
ð5Þ
where ε_ is the strain rate, R is the universal gas constant, T is the absolute temperature, Q is the activation energy, sp is the peak stress, and the rest of the parameters are the material constants. Formula (3) can be used for a wide range of stresses; formula (4) is favorable for low stresses and formula (5) for high stresses. Taking natural logarithms on both sides of formulae (4) and (5), the results are as follows: lnA0 þ n0 ln sp ¼ ln ε_ þ lnA″ þ βsp ¼ ln ε_ þ
Q RT
Q RT
ð6Þ ð7Þ
Fig. 4 presents the relation between ln ε: and ln sp or ln ε_ and sp. By averaging the slope of the lines in Fig. 4, β and n0 can be
calculated as 0.053 and 8.24 respectively. The dependence of α,
β and n0 is expressed as α ¼ β=n0
ð8Þ
So parameter α is determined as 0.0064. Taking natural logarithms on both sides of formula (1), formula (9) is obtained: ln ε_ þ
Q ¼ ln A þn ln ½ sinhðαsp Þ RT
ð9Þ
With the temperature unchanged, the plots of ln ε_ ln ½ sinhðαsp Þ are shown in Fig. 5a. The value of n can be determined by linear regression. The average of n corresponding to different temperatures is 6.13. Similarly, at a certain strain rate, the relation between ln[sin h (αsp)] and T 1 104 can be obtained with the assistance of peak stress and temperature, shown in Fig. 5b. A linear relation is recognizable and the slop of the line is Q/R. Taking the average value of Q/R, the activation energy Q is obtained as 308.85 kJ/mol. Compared with the previous work [14], Q of the tested steel is much higher than that of C–Mn steel or vanadium microalloyed steel. It has been reported that activation energy can be increased by vanadium addition [15]. It is also reported that vanadium addition in microalloyed steels seems to not affect the activation energy much. To facilitate the comparison, the tested steel without nitrogen is also tested and the activation energy Q is obtained as 276.39 kJ/mol by the same method. It can be inferred that nitrogen addition in vanadium microalloyed steel contributes to the higher
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B. Zhao et al. / Materials Science & Engineering A 604 (2014) 117–121
Fig. 5. ln ½ sinhðαsp Þ versus ln ε_ relation (a); ln ½ sinhðαsp Þ versus T 1 104 relation (b).
-0.6 -0.8 -1.0
5.4
εc εp
-1.2
5.0
lnσ
lnε
-1.4 -1.6
4.8
-1.8 -2.0
4.6
-2.2 -2.4 -2.6 24
σc σp
5.2
4.4 26
28
30
32
34
26
28
30
32
lnZ
lnZ Fig. 6. Relations between εp/εc and Z (a); sp/sc and Z (b).
activation energy. It can be explained that the interaction between nitrogen and vanadium in the steel affects the precipitation process of carbonitrides [16] and the process can be promoted by higher nitrogen addition [17] or by applying plastic deformation. Therefore, the precipitates play a pinning effect in the grain boundaries or subgrain boundaries and restrain dislocation movement, which retards the DRX process and results in a higher activation energy. With the assistance of the calculated parameters above, material constant A in formula (3) can be obtained as 2.11 1012; the hot working equation can be expressed as 308850 ð10Þ ε_ ¼ 2:11 1012 ½ sinhð0:064sp Þ6:13 exp RT
The relation between critical stress sc (strain εc) and Z or peak stress sp (strain εp) and Z is shown in Fig. 6. It can be seen that the ln sc (ln εc) or ln sp (εp) versus ln Z relation is linear and R is the linear correlation coefficient. By linear regression, the following formulas can be obtained:
sc ¼ 4:08315Z 0:12212
ð11Þ
sp ¼ 3:88312Z 0:12619
ð12Þ
εc ¼ 0:00918Z
ð13Þ
ð14Þ
It can be seen that an increase in the value of Z leads to higher value of sc(εc) or sp(εp). Therefore, it is hard for DRX to occur. On the contrary, with the decrease in Z, DRX can occur at a small strain.
3.5. DRX volume fraction DRX volume fraction X is often calculated with the assistance of the data from flow curves and expressed as the following: X¼
3.4. Critical conditions versus Zener–Hollomon relation
0:09539
εp ¼ 0:01050Z 0:11236
sp s sp ss
ð15Þ
where ss is the steady state stress, sp is the peak stress and s is the specific stress from flow curves. The formula is described in detail elsewhere [19]. In the present work, the X can be obtained by using formula (15). The following kinetic model of DRX is widely used [20]: ε εc n X ¼ 1 exp k ð16Þ εp where k and n are the material constants. To determine the constants, taking natural logarithms on both sides of formula (16) two times the corresponding formula can be
B. Zhao et al. / Materials Science & Engineering A 604 (2014) 117–121
121
increases with an increase in temperature, which is consistent with the effect of temperature on the peak value of the flow curves. The experimental curves in the dot form are also presented to facilitate the comparison. A good agreement is recognizable. Therefore, the kinetics model in the present work can predict the DRX volume fraction of the low carbon vanadium-nitride microalloyed steel with high resolution. 4. Conclusions The dynamic recrystallization behavior of a low carbon vanadium-nitride microalloyed steel was studied by performing single-pass compression tests on a Gleeble-3800 thermo-mechanical simulator. Based on the flow curves, the strain hardening rate versus stress relation was obtained and the critical conditions for initial DRX of the tested steel were determined, which resulted in the relation between the critical stress (strain) or peak stress (strain) and parameter Z. The activation energy, hot working equation and DRX kinetics model of the tested steel were obtained. The results were summarized as follows.
Fig. 7. ln ln(1/(1 X)) versus ln((ε εc)/εp) relation.
1. The tested steel exhibits a typical DRX behavior at higher deformation temperature and lower strain rate. 2. The critical stress (strain) versus peak stress (strain) relations were determined as sc ¼0.90285sp and εc ¼0.48046εp; the four parameters versus Z relations were established as sc ¼ 4.08315Z0.12212, sp ¼ 3.88312Z0.12619, εc ¼0.00918Z0.09539 and εp ¼0.01050Z0.11236. 3. The activation energy was 308.85 kJ/mol, which is higher than the steel without nitrogen or those in the previous works due to the higher nitrogen addition in the low carbon vanadium-nitride microalloyed steel. And the hot working equation was developed as ε_ ¼ 2.11 1012[sin h(0.064sp)]6.13exp( 308,850/RT). 4. The DRX kinetics model was obtained as X¼1 exp( 1.6526 (ε εc/εp)1.7994), which was compared with the experimental results. A high agreement is recognizable and the kinetics model is suitable to predict the DRX process of the tested steel. Fig. 8. Experimental and predicted results.
obtained: 1 ε εc ¼ ln k þ n ln ln ln 1X εp
References ð17Þ
It can be seen that the ln lnð1=ð1 XÞÞ versus lnððε εc Þ=εp Þ relation under different deformation conditions is almost linear; the slope of the line corresponds to the value of n and the intercept corresponds to the value of ln k. With the assistance of the experimental data, the ln lnð1=ð1 XÞÞ versus lnððε εc Þ=εp Þ relation can be obtained, as shown in Fig. 7. The values of k and n can be determined as 1.7994 and 1.6526 respectively. The kinetics model of DRX for the tested steel can be obtained. ! ε εc 1:7994 X ¼ 1 exp 1:6526 ð18Þ εp The effects of strain and temperature on the DRX volume fraction are shown in Fig. 8, the curves in solid. It can be seen that all the curves exhibit ‘S’ shapes. That means the DRX volume fraction increases slowly with an increase in strain at the beginning of deformation, markedly in the middle and then slowly near the end of deformation. Furthermore, the DRX volume fraction
[1] Lin Yongcheng, Chen Mingsong, Zhang Jun, Mater. Sci. Eng. A 499 (2009) 88–92. [2] H. Mirzadeh, J.M. Cabrera, J.M. Prado, A. Najafizadeh, Mater. Sci. Eng. A 528 (2011) 3876–3882. [3] M. Meysami, S.A.A.A. Mousavi, Mater. Sci. Eng. A 528 (2011) 3049–3055. [4] N.K. Balliger, W.K. Honeycombe, Metall.Trans. A 11 (1980) 421. [5] A.M. Sage, Met. Technol. 2 (1976) 65–70. [6] E.I. Poliak, J.J. Joans, Acta Mater. 44 (1996) 127–136. [7] E.I. Poliak, J.J. Jonas, ISIJ Int. 43 (2003) 686. [8] Y.G. Liu, M.Q. Li, J. Luo, Mater. Sci. Eng. A 574 (2013) 17–24. [9] C. Devadas, I.V. Samarasekera, E.B. Hawbolt, Metall. Trans. A 22 (1991) 335. [10] Y.W. Xu, D. Tang, Y. Song, X.G. Pan, Mater. Des. 39 (2012) 168–174. [11] H. Mirzadeh, A. Najafizadeh, Mater. Des. 31 (2010) 1174–1179. [12] Wei Hailian, Liu Guoquan, Xiao Xiang, Zhang Ming he, Mater. Sci. Eng. A 573 (2013) 166–174. [13] J.J. Jonas, C.M. Sellars, W.J. Tegart, Int. Met. Rev. 14 (1969) 1. [14] S.F. Medina, C.A. Hernandez, Acta Mater. 44 (1996) 137–148. [15] Zhou Xiaofeng, J. Plast. Eng. 14 (2007) 20–23. [16] R. Lagneborg, T. Siwecki, S. Zajac, Scand. J. Metall. 28 (1999) 186–241. [17] S. Zajac, T. Siwecki, M. Korchynsky, Conference Proceedings on Low Carbon Steels for the 90's. ASM/TSM, Pittsburgh, USA, 1993, pp. 139–150. [19] A. Momeni, H. Arabi, A. Rezaei, H. Badri, S.M. Abbasi, Mater. Sci. Eng. A 528 (2011) 2158–2163. [20] J. Wang, H. Xiao, H.B. Xie, X.M. Xu, Y.N. Gao, Mater. Sci. Eng. A 539 (2012) 294–300.
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
The kinetics of dynamic recrystallization of a low carbon vanadium-nitride microalloyed steel Baochun Zhao a,n, Tan Zhao a, Guiyan Li a, Qiang Lu b a b
Technology Center of Angang Steel Company Ltd., Anshan, Liaoning 114001, China Angang Steel Company Ltd., Bayuquan Subsidiary Company, Yingkou, Liaoning 115007, China
art ic l e i nf o
a b s t r a c t
Article history: Received 9 January 2014 Received in revised form 2 March 2014 Accepted 5 March 2014 Available online 12 March 2014
Single-pass compression tests were performed on a Gleeble-3800 thermo-mechanical simulator to study the dynamic recrystallization behavior of a low carbon vanadium-nitride microalloyed steel at the temperature in the range from 900 1C to 1050 1C and strain rate in the range from 0.1 s 1 to 10 s 1. Based on the flow curves from the tests, the effects of temperature and strain rate on the dynamic recrystallization behavior were analyzed. With the assistance of the process parameters, constitutive equations were used to obtain the activation energy and hot working equation. The strain hardening rate versus stress curves were used to determine the critical stress (strain) or the peak stress (strain). The dependence of the characteristic values on Zener–Hollomon was found. The dynamic recrystallization kinetics model of the tested steel was constructed and the validity was confirmed based on the experimental results. & 2014 Elsevier B.V. All rights reserved.
Keywords: Low carbon vanadium-nitride microalloyed steel Dynamic recrystallization Flow stress Mathematical model
1. Introduction Material microstructure evolution and flow behavior are complex during hot forming processes, which have a close relation to the shape of flow curves. Dynamic recovery (DRV), dynamic recrystallization (DRX) and static recrystallization (SRX) processes can be identified from the flow curves. Therefore, flow curves are often used to study the flow behavior of materials, which is also an efficient approach to study DRX behavior. Since DRX process contributes to grain refinement and lower stress, which play an important role in the formability, microstructure and mechanical properties of materials [1], it is of great practical importance to study the DRX that occurs during hot forming processes. At present, there are a considerable amount of researches on the DRX behavior of vanadium microalloyed steels or vanadium and titanium microalloyed steels [2,3]. In general, the steels with higher vanadium and lower nitrogen addition were tested. However, there are few researches on the steel with lower vanadium and higher nitrogen addition. Furthermore, it has been reported that nitrogen is a cost effective microalloyed element in vanadium microalloyed steel and it plays an important role in the effect of vanadium on the microstructure or properties of steels [4,5].
n Corresponding author at: Technology Center of Angang Steel Company Ltd., Anshan, Liaoning 114001, China. Tel.: þ86 41 2672 4152. E-mail address: [email protected] (B. Zhao).
http://dx.doi.org/10.1016/j.msea.2014.03.019 0921-5093/& 2014 Elsevier B.V. All rights reserved.
In the present work, single-pass compression tests were performed on a Gleeble-3800 thermo-mechanical simulator to study the DRX behavior of a low carbon vanadium-nitride microalloyed steel. Based on the flow curves, the effects of temperature and strain rate on the DRX behavior of the tested steel were analyzed. The DRX kinetics equations of the tested steel were established by the regression method. At last, the predicted results and experimental ones were compared.
2. Material and experiments In this work, the low carbon vanadium microalloyed steel with chemical composition of C 0.19, Mn 1.5, Si 0.37, V 0.06, Ti 0.019, S 0.0095, P 0.0087, N 0.0160 and balance iron (wt%) was used. The tested steel was from the continuous casting slab as received. The specimens with height of 12 mm and diameter of 8 mm were prepared. In order to reduce the occurrence of inhomogeneous compression, special anvils were employed. Both ends of the specimen were covered with tantalum foils to prevent adhesion between specimen and anvils. The specimens were austenitized at 1150 1C for 5 min and cooled with the rate of 5 1C/s to deformation temperature and held there for 1 min before compression. Single-pass compression tests were carried out at the temperature in the range from 900 to 1050 1C with an interval of 50 1C and strain rates of 0.1, 1, 3 and 10 s 1.
118
B. Zhao et al. / Materials Science & Engineering A 604 (2014) 117–121
3. Results and discussion 3.1. Flow curves analysis
mathematically smooth and there are some irregularities and fluctuations, which can make it impossible for the following differentiations. To eliminate the irregularities and fluctuations in the experimental curves, the flow curves were fitted by the ninth-order polynomial and good fitting curves were obtained. The resultant strain hardening rate θ versus stress curves are shown in Fig. 2. The inflection points and the zero points in the curves are marked out. Therefore, the critical stress sc (strain εc) or the peak stress sp (strain εp) can be obtained. Fig. 3 presents the relationship between sc (εc) and sp (εp). A linear relationship is recognizable and R is the linear correlation coefficient. By linear regression, the following formulas can be obtained:
Fig. 1 presents the flow curves under different deformation conditions. At the early stage of deformation, the stress increases proportionally to the strain, which leads to the increase in dislocation density and distortion in the steel. The strain hardening process is identified. At the second stage, the strain hardening effect can be reduced due to dislocation slipping, rearranging or eliminating. And the strain hardening rate keeps falling with the increase in strain. When the strain hardening rate is equal to zero, the stress reaches the peak. In Fig. 1, the flow curves exhibit typical peaks at the lower strain rate of 0.1 s 1. At the same strain rate and strain, the stress or the peak stress increases with the decrease in temperature. Since dislocation movement is restrained at lower temperature, it contributes to a higher strain hardening rate and results in a higher stress. At higher strain rate, strain hardening and dynamic recovery play the main role and no typical peak is recognizable. In Fig. 1b, it can be seen that the flow curve corresponding to strain hardening and dynamic recovery process is typical at a strain rate higher than 3 s 1.
In Sellars' research [9], the ratio of critical strain to peak strain generally falls in the range of 0.6–0.85. However, lower values for some microalloyed steel have been reported and they are in the range of 0.4–0.55 [10,11]. Since 0.4804 falls in the range, it is reasonable. Compared with the previous work on vanadium microalloyed steel [12], the value is higher, which maybe related to the higher nitrogen addition.
3.2. Determination of critical conditions
3.3. Activation energy and hot working equation
Poliak and Jonas [6,7] have proposed the critical condition kinetics based on the thermal irreversible principles and the critical conditions for the initiation of DRX can be determined by analyzing the relation between strain hardening rate and flow stress. It is a easier approach and widely used [7,8]. At the beginning of deformation, the softening induced by DRV is fast and strain hardening rate decreases with the increase of stress, which corresponds to the beginning of the sub-grain formation. At the second stage of deformation, the increase rate of softening rate decreases during the sub-grain forming process. When the stress reaches a critical value, the increase rate of softening rate suddenly increases due to onset of DRX, which leads to an inflection in the plot of strain hardening rate versus stress. The stress at the inflection point is identified as the critical stress. When a balance between strain hardening and softening reaches, the strain hardening rate would reduce to zero and the corresponding stress is identified as the peak stress. The flow curves under different deformation conditions were processed and analyzed by this method to determine the critical conditions of the tested steel. The experimental curves are not
The flow stress of material is related to process parameters and chemical compositions during hot working processes. With
sc ¼ 0:90285sp
ð1Þ
εc ¼ 0:48046εp
ð2Þ
Strain hardening rate θ
0.1s-1
σc
σp
Fig. 2. Strain hardening curves of the tested steel at different temperatures.
Fig. 1. Flow curves obtained for different deformation conditions.
B. Zhao et al. / Materials Science & Engineering A 604 (2014) 117–121
119
220 0.20
200
0.18
180
σc=0.90285σp
εc=0.48046εp
0.16
εc
σc
160 140
0.14
120
R=0.99253
0.12
100
0.10
80 80
100
120
140
160
σp
180
200
220
240
0.15
0.20
0.25
0.30
εp
0.35
0.40
.
3
3
2
2
1
1
ln (ε/s-1)
ln (ε/s-1)
Fig. 3. Relations between critical stress and peak stress (a); critical strain and peak strain (b).
0
.
-1 -2
0 -1 -2
-3 4.4
4.6
4.8
5.0
5.2
5.4
5.6
-3
80
100
120
140
ln(σp/Mpa)
160
180
200
220
240
260
σp/Mpa
Fig. 4. Relations between ln ε_ and ln sp (a); ln ε_ and sp (b).
chemical compositions unchanged, the dependence of temperature, strain rate and stress can be expressed as [13] Q ð3Þ A½ sinhðαsp Þn ¼ ε_ exp RT To obtain parameter α, the following formulas are also used: Q 0 A0 snp ¼ ε_ exp RT A″ expðβsp Þ ¼ ε_ exp
Q RT
ð4Þ
ð5Þ
where ε_ is the strain rate, R is the universal gas constant, T is the absolute temperature, Q is the activation energy, sp is the peak stress, and the rest of the parameters are the material constants. Formula (3) can be used for a wide range of stresses; formula (4) is favorable for low stresses and formula (5) for high stresses. Taking natural logarithms on both sides of formulae (4) and (5), the results are as follows: lnA0 þ n0 ln sp ¼ ln ε_ þ lnA″ þ βsp ¼ ln ε_ þ
Q RT
Q RT
ð6Þ ð7Þ
Fig. 4 presents the relation between ln ε: and ln sp or ln ε_ and sp. By averaging the slope of the lines in Fig. 4, β and n0 can be
calculated as 0.053 and 8.24 respectively. The dependence of α,
β and n0 is expressed as α ¼ β=n0
ð8Þ
So parameter α is determined as 0.0064. Taking natural logarithms on both sides of formula (1), formula (9) is obtained: ln ε_ þ
Q ¼ ln A þn ln ½ sinhðαsp Þ RT
ð9Þ
With the temperature unchanged, the plots of ln ε_ ln ½ sinhðαsp Þ are shown in Fig. 5a. The value of n can be determined by linear regression. The average of n corresponding to different temperatures is 6.13. Similarly, at a certain strain rate, the relation between ln[sin h (αsp)] and T 1 104 can be obtained with the assistance of peak stress and temperature, shown in Fig. 5b. A linear relation is recognizable and the slop of the line is Q/R. Taking the average value of Q/R, the activation energy Q is obtained as 308.85 kJ/mol. Compared with the previous work [14], Q of the tested steel is much higher than that of C–Mn steel or vanadium microalloyed steel. It has been reported that activation energy can be increased by vanadium addition [15]. It is also reported that vanadium addition in microalloyed steels seems to not affect the activation energy much. To facilitate the comparison, the tested steel without nitrogen is also tested and the activation energy Q is obtained as 276.39 kJ/mol by the same method. It can be inferred that nitrogen addition in vanadium microalloyed steel contributes to the higher
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Fig. 5. ln ½ sinhðαsp Þ versus ln ε_ relation (a); ln ½ sinhðαsp Þ versus T 1 104 relation (b).
-0.6 -0.8 -1.0
5.4
εc εp
-1.2
5.0
lnσ
lnε
-1.4 -1.6
4.8
-1.8 -2.0
4.6
-2.2 -2.4 -2.6 24
σc σp
5.2
4.4 26
28
30
32
34
26
28
30
32
lnZ
lnZ Fig. 6. Relations between εp/εc and Z (a); sp/sc and Z (b).
activation energy. It can be explained that the interaction between nitrogen and vanadium in the steel affects the precipitation process of carbonitrides [16] and the process can be promoted by higher nitrogen addition [17] or by applying plastic deformation. Therefore, the precipitates play a pinning effect in the grain boundaries or subgrain boundaries and restrain dislocation movement, which retards the DRX process and results in a higher activation energy. With the assistance of the calculated parameters above, material constant A in formula (3) can be obtained as 2.11 1012; the hot working equation can be expressed as 308850 ð10Þ ε_ ¼ 2:11 1012 ½ sinhð0:064sp Þ6:13 exp RT
The relation between critical stress sc (strain εc) and Z or peak stress sp (strain εp) and Z is shown in Fig. 6. It can be seen that the ln sc (ln εc) or ln sp (εp) versus ln Z relation is linear and R is the linear correlation coefficient. By linear regression, the following formulas can be obtained:
sc ¼ 4:08315Z 0:12212
ð11Þ
sp ¼ 3:88312Z 0:12619
ð12Þ
εc ¼ 0:00918Z
ð13Þ
ð14Þ
It can be seen that an increase in the value of Z leads to higher value of sc(εc) or sp(εp). Therefore, it is hard for DRX to occur. On the contrary, with the decrease in Z, DRX can occur at a small strain.
3.5. DRX volume fraction DRX volume fraction X is often calculated with the assistance of the data from flow curves and expressed as the following: X¼
3.4. Critical conditions versus Zener–Hollomon relation
0:09539
εp ¼ 0:01050Z 0:11236
sp s sp ss
ð15Þ
where ss is the steady state stress, sp is the peak stress and s is the specific stress from flow curves. The formula is described in detail elsewhere [19]. In the present work, the X can be obtained by using formula (15). The following kinetic model of DRX is widely used [20]: ε εc n X ¼ 1 exp k ð16Þ εp where k and n are the material constants. To determine the constants, taking natural logarithms on both sides of formula (16) two times the corresponding formula can be
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increases with an increase in temperature, which is consistent with the effect of temperature on the peak value of the flow curves. The experimental curves in the dot form are also presented to facilitate the comparison. A good agreement is recognizable. Therefore, the kinetics model in the present work can predict the DRX volume fraction of the low carbon vanadium-nitride microalloyed steel with high resolution. 4. Conclusions The dynamic recrystallization behavior of a low carbon vanadium-nitride microalloyed steel was studied by performing single-pass compression tests on a Gleeble-3800 thermo-mechanical simulator. Based on the flow curves, the strain hardening rate versus stress relation was obtained and the critical conditions for initial DRX of the tested steel were determined, which resulted in the relation between the critical stress (strain) or peak stress (strain) and parameter Z. The activation energy, hot working equation and DRX kinetics model of the tested steel were obtained. The results were summarized as follows.
Fig. 7. ln ln(1/(1 X)) versus ln((ε εc)/εp) relation.
1. The tested steel exhibits a typical DRX behavior at higher deformation temperature and lower strain rate. 2. The critical stress (strain) versus peak stress (strain) relations were determined as sc ¼0.90285sp and εc ¼0.48046εp; the four parameters versus Z relations were established as sc ¼ 4.08315Z0.12212, sp ¼ 3.88312Z0.12619, εc ¼0.00918Z0.09539 and εp ¼0.01050Z0.11236. 3. The activation energy was 308.85 kJ/mol, which is higher than the steel without nitrogen or those in the previous works due to the higher nitrogen addition in the low carbon vanadium-nitride microalloyed steel. And the hot working equation was developed as ε_ ¼ 2.11 1012[sin h(0.064sp)]6.13exp( 308,850/RT). 4. The DRX kinetics model was obtained as X¼1 exp( 1.6526 (ε εc/εp)1.7994), which was compared with the experimental results. A high agreement is recognizable and the kinetics model is suitable to predict the DRX process of the tested steel. Fig. 8. Experimental and predicted results.
obtained: 1 ε εc ¼ ln k þ n ln ln ln 1X εp
References ð17Þ
It can be seen that the ln lnð1=ð1 XÞÞ versus lnððε εc Þ=εp Þ relation under different deformation conditions is almost linear; the slope of the line corresponds to the value of n and the intercept corresponds to the value of ln k. With the assistance of the experimental data, the ln lnð1=ð1 XÞÞ versus lnððε εc Þ=εp Þ relation can be obtained, as shown in Fig. 7. The values of k and n can be determined as 1.7994 and 1.6526 respectively. The kinetics model of DRX for the tested steel can be obtained. ! ε εc 1:7994 X ¼ 1 exp 1:6526 ð18Þ εp The effects of strain and temperature on the DRX volume fraction are shown in Fig. 8, the curves in solid. It can be seen that all the curves exhibit ‘S’ shapes. That means the DRX volume fraction increases slowly with an increase in strain at the beginning of deformation, markedly in the middle and then slowly near the end of deformation. Furthermore, the DRX volume fraction
[1] Lin Yongcheng, Chen Mingsong, Zhang Jun, Mater. Sci. Eng. A 499 (2009) 88–92. [2] H. Mirzadeh, J.M. Cabrera, J.M. Prado, A. Najafizadeh, Mater. Sci. Eng. A 528 (2011) 3876–3882. [3] M. Meysami, S.A.A.A. Mousavi, Mater. Sci. Eng. A 528 (2011) 3049–3055. [4] N.K. Balliger, W.K. Honeycombe, Metall.Trans. A 11 (1980) 421. [5] A.M. Sage, Met. Technol. 2 (1976) 65–70. [6] E.I. Poliak, J.J. Joans, Acta Mater. 44 (1996) 127–136. [7] E.I. Poliak, J.J. Jonas, ISIJ Int. 43 (2003) 686. [8] Y.G. Liu, M.Q. Li, J. Luo, Mater. Sci. Eng. A 574 (2013) 17–24. [9] C. Devadas, I.V. Samarasekera, E.B. Hawbolt, Metall. Trans. A 22 (1991) 335. [10] Y.W. Xu, D. Tang, Y. Song, X.G. Pan, Mater. Des. 39 (2012) 168–174. [11] H. Mirzadeh, A. Najafizadeh, Mater. Des. 31 (2010) 1174–1179. [12] Wei Hailian, Liu Guoquan, Xiao Xiang, Zhang Ming he, Mater. Sci. Eng. A 573 (2013) 166–174. [13] J.J. Jonas, C.M. Sellars, W.J. Tegart, Int. Met. Rev. 14 (1969) 1. [14] S.F. Medina, C.A. Hernandez, Acta Mater. 44 (1996) 137–148. [15] Zhou Xiaofeng, J. Plast. Eng. 14 (2007) 20–23. [16] R. Lagneborg, T. Siwecki, S. Zajac, Scand. J. Metall. 28 (1999) 186–241. [17] S. Zajac, T. Siwecki, M. Korchynsky, Conference Proceedings on Low Carbon Steels for the 90's. ASM/TSM, Pittsburgh, USA, 1993, pp. 139–150. [19] A. Momeni, H. Arabi, A. Rezaei, H. Badri, S.M. Abbasi, Mater. Sci. Eng. A 528 (2011) 2158–2163. [20] J. Wang, H. Xiao, H.B. Xie, X.M. Xu, Y.N. Gao, Mater. Sci. Eng. A 539 (2012) 294–300.